the corresponding cumulative distribution function figure is picked from 

 Figures 37 through 48. The coordinate value on the vertical axis of the 

 distribution function which equals the uniform random number is located. 

 Reading horizontally from this coordinate value to the empirical distrib- 

 ution curve and then down vertically to the SNR axis yields a random SNR 

 value. This procedure is illustrated in Figure 37 by the dotted line. 

 The uniform random number is 0.532. The corresponding random SNR value 

 is -0.16. 



The distribution function for the SNR values obtained by this proce- 

 dure will be identical to the graphed empirical distribution function 

 FcmdCw). This follows from the following argument. The SNR, so developed 



are less than or equal to w if, and only if, the uniform random number 

 is less than or equal to FsNR '■"-'■ This is true because the two numbers 

 are tied together via the graphed curve^. Hence, 



P [random SNR £ w] = P [U < Fgj^f^Cw)] , (45) 



where IJ denotes the uniform random number. But by definition, the dis- 

 tribution function for a uniform random number is: 



F^(u) = P [U £ u] = u . (46) 



Hence, returning to equation (45), 



P [random SNR < w] = 'P (U f FsNR^^"^] = ^SNR^^^^ • ^^'^^ 



The above procedure is repeated for 300 independent uniform random 

 numbers to obtain 300 random SNR values. These 300 SNR values are just 

 as likely to have happened as the originally occurring values, provided 

 the decomposition in equation (39) is accepted as valid and provided the 

 independence assumption truly holds. 



Hence, equation (39) can be used with the 300 SNR values and the 

 p(fj^), a+ ni' ^"<^ ^- m frequency functions to create a new set of 

 spectral lines, p*(f ). These spectral lines might just as well occurred 

 as the original set if the random spectral fluctuations had accidentally 

 gone that way. 



Finally, the 300 simulated spectral lines, p*(fj^), are smoothed 

 according to equation (31) to produce new simulated spectral densities, 



^(fm)- 



The above procedure in its entirety was repeated 900 times for each 

 of the 12 pieces of Hurricane Carla data. Thus, 900 statistically equiva- 

 lent spectral densities were generated by simulation for each hurricane 

 data record. 



63 



